Accurate Ab-initio Neural-network Solutions to Large-Scale Electronic Structure Problems

TL;DR

FiRE bridges a key gap in ab-initio calculations by combining the scalability of conventional VMC with the accuracy of NN-VMC. It introduces finite-range embeddings to restrict electron interactions, reducing per-step cost to $O(n_{el}^3)$ and yielding roughly a $10\times$ speedup for systems with hundreds of electrons, while preserving chemical accuracy. The method demonstrates competitive relative energies across non-covalent interactions, singlet-triplet gaps, and organometallic energetics, often rivaling or surpassing CCSD(T) and AFQMC benchmarks. Convergence analyses reveal robust polynomial scaling with $\alpha\approx1$ and $\beta\approx2.3$, suggesting practical optimization for large systems and broad applicability to chemistry and materials science.

Abstract

We present finite-range embeddings (FiRE), a novel wave function ansatz for accurate large-scale ab-initio electronic structure calculations. Compared to contemporary neural-network wave functions, FiRE reduces the asymptotic complexity of neural-network variational Monte Carlo (NN-VMC) by $\sim n_\text{el}$, the number of electrons. By restricting electron-electron interactions within the neural network, FiRE accelerates all key operations -- sampling, pseudopotentials, and Laplacian computations -- resulting in a real-world $10\times$ acceleration in now-feasible 180-electron calculations. We validate our method's accuracy on various challenging systems, including biochemical compounds, conjugated hydrocarbons, and organometallic compounds. On these systems, FiRE's energies are consistently within chemical accuracy of the most reliable data, including experiments, even in cases where high-accuracy methods such as CCSD(T), AFQMC, or contemporary NN-VMC fall short. With these improvements in both runtime and accuracy, FiRE represents a new `gold-standard' method for fast and accurate large-scale ab-initio calculations, potentially enabling new computational studies in fields like quantum chemistry, solid-state physics, and material design.

Figures (9)

• Figure 1: Conceptual overview: a) For each-single electron move, e.g., during sampling or pseudopotentials, we only update the orbitals of electrons within the cutoff of its old and new positions. b) FiRE enables efficient Laplacian computations by exploiting the sparsity patterns within the Jacobian $\nabla {\Phi}({{\bm{r}}})$ to only compute non-zero entries. c) All components of VMC that are accelerated by FiRE.
• Figure 2: Runtime for cumulene chains of varying length. Runtimes for equivalent batch size of 4096 on a single A100 GPU. FiRE models use a cutoff ${c}=3a_0$a) Time required to update the wave function $\Psi$ after single-electron move. b) Time required to compute the kinetic energy $\Delta \Psi$. c) Total time per optimization step. d) Breakdown of the runtime of a single optimization step for different architectures.
• Figure 3: Relative energies on a series of challenging strongly-correlated systems. a) Energy deviations versus CCSD(T) for non-covalent interaction energies of 11 systems of the S22 dataset jureckaBenchmarkDatabaseAccurate2006marshallBasisSetConvergence2011. b) Detailed comparison of benzene dimer interaction energy across methods. c) Singlet-triplet energy gap in $n$-acene from naphthalene to hexacene. d)$n$-acene energy gap error to ZPVE corrected experimental results anglikerElectronicSpectraHexacene1982cbirksPhotophysicsAromaticMolecules1970burgosHeterofissionPentacenedopedTetracene1977aschiedtPhotodetachmentPhotoelectronSpectroscopy1997siebrandRadiationlessTransitionsPolyatomic1967. Shaded region corresponds to typical experimental uncertainty: ±1kcal/mol for S22 (a) and acenes (c-d), and experimental uncertainty for benzene dimer (b).
• Figure 4: Organometallic compounds: a) Ionization potential of chloroferrocene as a function of optimization steps. b) Mean absolute error for protonation of iron-sulfur complex for conventional methods and FiRE. Inset: relative energies of 3 protonation sites vs HC site.
• Figure 5: Convergence rates for neural wave functions: Absolute energy error as a function of optimization steps for molecules of increasing size: a) cumulenes b) acenes. For both systems, the optimization curves are well approximated by a powerlaw with similar exponents.